What is an example of a better board that I can get shipped to my home for under $50 USD?
Price
Performance
Exposed I/O
Device Size
Community Size
I don't know of any board that beats the Pi on more than 3 of these attributes.
The allwinner sticks you mentioned are comparably priced, but have a smaller development community and very limited I/O. If all you want is a little media player, I think they are a good choice though.
http://liliputing.com/2012/07/allwinner-pledges-support-for-...
As for lower level development, you are probably right, few boards can claim to beat the Pi.